From Fermat To Minkowski

Author : W. Scharlau,H. Opolka
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 52,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475718676

Get Book

From Fermat to Minkowski by W. Scharlau,H. Opolka Pdf

This book arose from a course of lectures given by the first author during the winter term 1977/1978 at the University of Münster (West Germany). The course was primarily addressed to future high school teachers of mathematics; it was not meant as a systematic introduction to number theory but rather as a historically motivated invitation to the subject, designed to interest the audience in number-theoretical questions and developments. This is also the objective of this book, which is certainly not meant to replace any of the existing excellent texts in number theory. Our selection of topics and examples tries to show how, in the historical development, the investigation of obvious or natural questions has led to more and more comprehensive and profound theories, how again and again, surprising connections between seemingly unrelated problems were discovered, and how the introduction of new methods and concepts led to the solution of hitherto unassailable questions. All this means that we do not present the student with polished proofs (which in turn are the fruit of a long historical development); rather, we try to show how these theorems are the necessary consequences of natural questions. Two examples might illustrate our objectives.

Author : W. Scharlau,H. Opolka
Publisher : Unknown
Page : 200 pages
File Size : 48,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475718683

Get Book

From Fermat to Minkowski by W. Scharlau,H. Opolka Pdf

Author : Winfried Scharlau,Hans Opolka
Publisher : Unknown
Page : 184 pages
File Size : 55,9 Mb
Release : 1985
Category : Number theory
ISBN : 3540909427

Get Book

From Fermat to Minkowski by Winfried Scharlau,Hans Opolka Pdf

Author : Michal Krizek,Florian Luca,Lawrence Somer
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 42,6 Mb
Release : 2002-01-08
Category : Mathematics
ISBN : 0387953329

Get Book

17 Lectures on Fermat Numbers by Michal Krizek,Florian Luca,Lawrence Somer Pdf

The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.

Author : Kristine K. Fowler
Publisher : CRC Press
Page : 412 pages
File Size : 46,5 Mb
Release : 2004-05-25
Category : Language Arts & Disciplines
ISBN : 0824750357

Get Book

Using the Mathematics Literature by Kristine K. Fowler Pdf

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

Author : Israel Kleiner
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 53,8 Mb
Release : 2012-02-02
Category : Mathematics
ISBN : 9780817682682

Get Book

Excursions in the History of Mathematics by Israel Kleiner Pdf

This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.

Author : Shigeru Kanemitsu,Chaohua Jia
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 40,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475736755

Get Book

Number Theoretic Methods by Shigeru Kanemitsu,Chaohua Jia Pdf

This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the National Science Foundation of China (NSFC), and some invited papers of eminent number-theorists who visited Japan during 1999-2001 at the occasion of the Conference at the Research Institute of Mathematical Sciences (RIMS), Kyoto University. The proceedings of the 1st China-Japan Seminar held in September 1999 in Beijing has been published recently {2002) by Kluwer as DEVM 6 which also contains some invited papers. The topics of that volume are, however, restricted to analytic number theory and many papers in this field are assembled. In this volume, we return to the lines of the previous one "Number Theory and its Applications", published as DEVM 2 by Kluwer in 1999 and uphold the spirit of presenting various topics in number theory and related areas with possible applica tions, in a unified manner, and this time in nearly a book form with a well-prepared index. We accomplish this task by collecting highly informative and readable survey papers (including half-survey type papers), giving overlooking surveys of the hith erto obtained results in up-to-the-hour form with insight into the new developments, which are then analytically continued to a collection of high standard research papers which are concerned with rather diversed areas and will give good insight into new researches in the new century.

Author : Falko Lorenz
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 47,7 Mb
Release : 2006-07-02
Category : Mathematics
ISBN : 9780387316086

Get Book

Algebra by Falko Lorenz Pdf

This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.

Author : Max-Albert Knus
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642754012

Get Book

Quadratic and Hermitian Forms over Rings by Max-Albert Knus Pdf

From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued, notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book.

Author : Franz Lemmermeyer
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 51,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662128930

Get Book

Reciprocity Laws by Franz Lemmermeyer Pdf

This book covers the development of reciprocity laws, starting from conjectures of Euler and discussing the contributions of Legendre, Gauss, Dirichlet, Jacobi, and Eisenstein. Readers knowledgeable in basic algebraic number theory and Galois theory will find detailed discussions of the reciprocity laws for quadratic, cubic, quartic, sextic and octic residues, rational reciprocity laws, and Eisensteins reciprocity law. An extensive bibliography will be of interest to readers interested in the history of reciprocity laws or in the current research in this area.

Author : Jeremy Gray
Publisher : Springer
Page : 350 pages
File Size : 44,8 Mb
Release : 2015-10-14
Category : Mathematics
ISBN : 9783319237152

Get Book

The Real and the Complex: A History of Analysis in the 19th Century by Jeremy Gray Pdf

This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis.

Author : H. E. Rose
Publisher : Oxford University Press
Page : 420 pages
File Size : 48,9 Mb
Release : 1995
Category : Mathematics
ISBN : 0198523769

Get Book

A Course in Number Theory by H. E. Rose Pdf

This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.

Author : Michael C. Berg
Publisher : John Wiley & Sons
Page : 118 pages
File Size : 51,8 Mb
Release : 2011-09-30
Category : Mathematics
ISBN : 9781118031193

Get Book

The Fourier-Analytic Proof of Quadratic Reciprocity by Michael C. Berg Pdf

A unique synthesis of the three existing Fourier-analytictreatments of quadratic reciprocity. The relative quadratic case was first settled by Hecke in 1923,then recast by Weil in 1964 into the language of unitary grouprepresentations. The analytic proof of the general n-th order caseis still an open problem today, going back to the end of Hecke'sfamous treatise of 1923. The Fourier-Analytic Proof of QuadraticReciprocity provides number theorists interested in analyticmethods applied to reciprocity laws with a unique opportunity toexplore the works of Hecke, Weil, and Kubota. This work brings together for the first time in a single volume thethree existing formulations of the Fourier-analytic proof ofquadratic reciprocity. It shows how Weil's groundbreakingrepresentation-theoretic treatment is in fact equivalent to Hecke'sclassical approach, then goes a step further, presenting Kubota'salgebraic reformulation of the Hecke-Weil proof. Extensivecommutative diagrams for comparing the Weil and Kubotaarchitectures are also featured. The author clearly demonstrates the value of the analytic approach,incorporating some of the most powerful tools of modern numbertheory, including adèles, metaplectric groups, andrepresentations. Finally, he points out that the critical commonfactor among the three proofs is Poisson summation, whosegeneralization may ultimately provide the resolution for Hecke'sopen problem.

Author : W. Scharlau
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642699719

Get Book

Quadratic and Hermitian Forms by W. Scharlau Pdf

For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. Much of the best work of the great number theorists of the eighteenth and nineteenth century was concerned with problems about quadratic forms. On the basis of their work, Minkowski, Siegel, Hasse, Eichler and many others crea ted the impressive "arithmetic" theory of quadratic forms, which has been the object of the well-known books by Bachmann (1898/1923), Eichler (1952), and O'Meara (1963). Parallel to this development the ideas of abstract algebra and abstract linear algebra introduced by Dedekind, Frobenius, E. Noether and Artin led to today's structural mathematics with its emphasis on classification problems and general structure theorems. On the basis of both - the number theory of quadratic forms and the ideas of modern algebra - Witt opened, in 1937, a new chapter in the theory of quadratic forms. His most fruitful idea was to consider not single "individual" quadratic forms but rather the entity of all forms over a fixed ground field and to construct from this an algebra ic object. This object - the Witt ring - then became the principal object of the entire theory. Thirty years later Pfister demonstrated the significance of this approach by his celebrated structure theorems.

Author : Don Redmond
Publisher : CRC Press
Page : 778 pages
File Size : 43,5 Mb
Release : 1996-04-23
Category : Mathematics
ISBN : 0824796969

Get Book

Number Theory by Don Redmond Pdf

This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.